Inverse Time Limit Theory (ITLT)

Inverse Time Limit Theory (ITLT) presents a fully regular black hole solution derived from the Einstein–Hilbert action through a minisuperspace reduction under static spherical symmetry. Instead of postulating an ad hoc metric ansatz, the mass function is promoted to a radial degree of freedom, and regularity at the origin is imposed as a physical constraint. The resulting spacetime is described by the metric functionf(r) = 1 − 2M r² / (r³ + a)where M is the ADM mass and a controls the core scale.The geometry is asymptotically Schwarzschild and contains a de Sitter–like regular core. All curvature invariants, including the Ricci scalar and Kretschmann scalar, remain finite at r = 0.The effective stress–energy tensor satisfies the weak energy condition, while the strong energy condition is violated only within the core region, as required for singularity avoidance. The horizon structure admits two horizons, an extremal configuration, or a horizonless phase depending on parameters. Extremality occurs ata = 32M³ / 27and leads to a zero-temperature configuration with finite horizon radius, implying the existence of a stable remnant.Linear axial perturbation analysis using the Regge–Wheeler equation demonstrates dynamical stability. The effective potential is positive definite and diverges near the core, preventing unstable modes.A complete geodesic analysis shows that all timelike and null geodesics extend smoothly through r = 0. The spacetime is therefore globally geodesically complete. The Penrose diagram resembles Reissner–Nordström in horizon structure but contains no spacelike singularity; the central region is regular and timelike.The model admits a covariant scalar–tensor embedding free of ghost instabilities and reproduces standard Schwarzschild behavior at large distances, with controlled higher-order corrections.Observable consequences include:• Small horizon radius shift• Modified photon sphere• Deviations in quasinormal modes• Finite-temperature endpoint of evaporationITLT provides a mathematically consistent, dynamically stable, and thermodynamically complete regular black hole model derived from first principles.